Saturday, June 11, 2011

Three Routes To Choice

A theme of this blog is the incorrectness of the neoclassical textbook description of how agents choose. The assumptions of this view can be stated as:

An agent knows the complete list of choices from which they must select.

Given any two elements from this space of choices, the agent knows whether one of these elements is not preferred to the other.

Any element from this space is not preferred to itself.

The ranking obtained from the preference relation is transitive.

If the space of choices is a continuum, a certain continuity assumption must hold for the preference relation so as to rule out lexicographic preferences.

These assumptions supposedly imply the claim that utility attains at most an ordinal measurement scale level1. And they allow one to derive the demand for consumer goods and the supply of factors of production.

Economists have transcended this framework. I have previously pointed out models of agents as consisting of multiple selves. I think this approach exhibits a consilience with theories in, for example, cognitive psychology. I have recently stumbled upon two other ways of modeling choice, generalizing the textbook view to an approach more consistent with empirical evidence from behavioral economics and that cannot be justifiably characterized as "irrational".

Nadeem Naqvi has developed an approach of incorporating tertiary information into choice. In the outdated neoclassical theory, one might represent the relationship y is not preferred to x for agent i by:

xRiy

Naqvi and his colleaques introduce the relation Ri(Vij), where Vij is the background set for agent i. Parametric variation in the agent’s background set can alter the agent’s preferences. That is, one can have, for l ≠ m:

xRi(Vil) y

and

yRi(Vim) x

One interesting consequence of this modeling strategy is that racial discrimination is formally consistent with Pareto optimality. This "is a surprising, though serious, indictment of relying exclusively on the Pareto principle in social evaluation."

Gul and Pesendorfer consider choice among menus. They consider an agent who is a vegetarian for health reasons, but who is tempted to choose hamburgers, if available. In choosing a restaurant at noon, they would prefer a restaurant with hamburgers on the menu. But in choosing in the morning a restaurant to visit at noon, they will select one with an all-vegtable menu. I hope you can see how this approach allows one to analyze time-consistency of choices.

How long do you think before such approaches are presented in mainstream textbooks in widespread use?

Footnotes:1 Nominal, ordinal, interval, and ratio are well-known measurement scale level, where a level is defined up to a set of transformations. I find curious the claim that the expression of the marginal rate of transformation as a ratio of marginal utilities is consistent with an ordinal scale. Mirowski, in More Heat Than Light has also raised questions about the claim that utility only attains an ordinal scale level. I recently stumbled upon Mandler (2006), where he suggests, not necessarily for related reasons, utility be considered to attain a measurement scale level between ordinal and interval.